This dissertation aims to develop statistical methodologies for estimating the effects of time-fixed and time-varying factors in recurrent events modeling context. The research is motivated by the traffic safety research question of evaluating the influence of crash on driving risk and driver behavior. The methodologies developed, however, are general and can be applied to other fields. Four alternative approaches based on various data settings are elaborated and applied to 100-Car Naturalistic Driving Study in the following Chapters. Chapter 1 provides a general introduction and background of each method, with a sketch of 100-Car Naturalistic Driving Study. In Chapter 2, I assessed the impact of crash on driving behavior by comparing the frequency of distraction events in per-defined windows. A count-based approach based on mixed-effect binomial regression models was used. In Chapter 3, I introduced intensity-based recurrent event models by treating number of Safety Critical Incidents and Near Crash over time as a counting process. Recurrent event models fit the natural generation scheme of the data in this study. Four semi-parametric models are explored: Andersen-Gill model, Andersen-Gill model with stratified baseline functions, frailty model, and frailty model with stratified baseline functions. I derived model estimation procedure and and conducted model comparison via simulation and application. The recurrent event models in Chapter 3 are all based on proportional assumption, where effects are constant. However, the change of effects over time is often of primary interest. In Chapter 4, I developed time-varying coefficient model using penalized B-spline function to approximate varying coefficients. Shared frailty terms was used to incorporate correlation within subjects. Inference and statistical test are also provided. Frailty representation was proposed to link time-varying coefficient model with regular frailty model. In Chapter 5, I further extended framework to accommodate multi-type recurrent events with time-varying coefficient. Two types of recurrent-event models were developed. These models incorporate correlation among intensity functions from different type of events by correlated frailty terms. Chapter 6 gives a general review on the contributions of this dissertation and discussion of future research directions. / Ph. D.

In this dissertation, we introduce three projects in machine learning and reliability applications after the general introductions in Chapter 1. The first project concentrates on the multivariate sensory data, the second project is related to the bivariate recurrent process, and the third project introduces thermal index (TI) estimation in accelerated destructive degradation test (ADDT) data, in which an R package is developed. All three projects are related to and can be used to solve certain reliability problems. Specifically, in Chapter 2, we introduce a clustering method for multivariate functional data. In order to cluster the customized events extracted from multivariate functional data, we apply the functional principal component analysis (FPCA), and use a model based clustering method on a transformed matrix. A penalty term is imposed on the likelihood so that variable selection is performed automatically. In Chapter 3, we propose a covariate-adjusted model to predict next event in a bivariate recurrent event system. Inspired by geyser eruptions in Yellowstone National Park, we consider two event types and model their event gap time relationship. External systematic conditions are taken account into the model with covariates. The proposed covariate adjusted recurrent process (CARP) model is applied to the Yellowstone National Park geyser data. In Chapter 4, we compare estimation methods for TI. In ADDT, TI is an important index indicating the reliability of materials, when the accelerating variable is temperature. Three methods are introduced in TI estimations, which are least-squares method, parametric model and semi-parametric model. An R package is implemented for all three methods. Applications of R functions are introduced in Chapter 5 with publicly available ADDT datasets. Chapter 6 includes conclusions and areas for future works. / Doctor of Philosophy / This dissertation focuses on three projects that are all related to machine learning and reliability. Specifically, in the first project, we propose a clustering method designated for events extracted from multivariate sensory data. When the customized event is corresponding to reliability issues, such as aging procedures, clustering results can help us learn different event characteristics by examining events belonging to the same group. Applications include diving behavior segmentation based on vehicle sensory data, where multiple sensors are measuring vehicle conditions simultaneously and events are defined as vehicle stoppages. In our project, we also proposed to conduct sensor selection by three different penalizations including individual, variable and group. Our method can be applied for multi-dimensional sensory data clustering, when optimal sensor design is also an objective. The second project introduces a covariate-adjusted model accommodated to a bivariate recurrent event process system. In such systems, events can occur repeatedly and event occurrences for each type can affect each other with certain dependence. Events in the system can be mechanical failures which is related to reliability, while next event time and type predictions are usually of interest. Precise predictions on the next event time and type can essentially prevent serious safety and economy consequences following the upcoming event. We propose two CARP models with marginal behaviors as well as the dependence structure characterized in the bivariate system. We innovate to incorporate external information to the model so that model results are enhanced. The proposed model is evaluated in simulation studies, while geyser data from Yellowstone National Park is applied. In the third project, we comprehensively discuss three estimation methods for thermal index. They are the least-square method, parametric model and semi-parametric model. When temperature is the accelerating variable, thermal index indicates the temperature at which our materials can hold up to a certain time. In reality, estimating the thermal index precisely can prolong lifetime of certain product by choosing the right usage temperature. Methods evaluations are conducted by simulation study, while applications are applied to public available datasets.

In modern communication systems, it’s important to detect and use available radio frequencies effectively. However, current methods face challenges with complexity and noise interference. We’ve developed a new approach using advanced artificial intelligence (AI) based computing techniques to improve efficiency and accuracy in this process. Our method shows promising results, requiring only minimal additional resources in exchange of improved performance compared to older techniques. / Master of Science / In modern communication systems, it’s important to detect and use available radio frequencies effectively. However, current methods face challenges with complexity and noise interference. We’ve developed a new approach using advanced artificial intelligence (AI) based computing techniques to improve efficiency and accuracy in this process. Our method shows promising results, requiring only minimal additional resources in exchange of improved performance compared to older techniques.

Loss reserving in P&C insurance, is the common practice of estimating the insurer’s liability from future claims it will have to pay out on. In the recent years, it has been popular to explore the options of forecasting this loss with the help of machine learning methods. This is mainly attributed to the increase in computational power, opening up opportunities for handling more complex computations with large datasets. The main focus of this paper is to implement and evaluate a recurrent neural network called the deeptriangle by Kuo for modelling payments of individual reported but not settled claims. The results are compared with the traditional Chain Ladder method and a baseline model on a simulated dataset provided by Wüthrich’s simulation machine.  The models were implemented in Python using Tensorflow’s functional API. The results show that the recurrent neural network does not outperform the Chain Ladder method on the given data. The recurrent neural network is weak towards the sparse and chaotic nature of individual claim payments and is unable to detect a stable sequential pattern. Results also show that the neural network is prone to overfitting, which can theoretically be compensated with larger dataset but comes at a cost in terms of feasibility. / Reservsättning inom skadeförsäkring handlar om att beräkna framtida kostnader av en försäkringsgivare. Under de senaste åren har det blivit allt populärare att undersöka tillämpningen av olika statistiska inlärningsmetoder inom reservsättning. Den här uppsatsen syftar till att implementera och utvärdera ett återkommande neuraltnätverk som kallas för ”deeptriangle by Kuo” för att modellera utbetalningar av individuella rapporterade men icke­ färdigbetalda försäkringsfordringar. Resultaten kommer att jämföras med den traditionella Chain Ladder metoden samt en grundmodell på ett simulerat dataset som tillhandahålls av ”Wüthrichs simulation machine”. Modellerna implementeras i Python med hjälp av Tensorflows Functional API. Resultatet är att det återkommande neurala nätverket inte överträffar Chain Ladder metoden med den givna datan. Det återkommande neurala nätverket har svårigheter för att känna igen mönster i datamängder som individuella skadebetalningar eftersom datamängden till sin natur är spridd och kaotisk. Resultaten visar också att det neurala nätverket är benäget att överanpassa, vilket teoretiskt kan kompenseras med en större datamängd men som i sin tur bidrar till en risk för ogenomförbarhet.

Cotutelle entre l’université de Montréal et d’Aix-Marseille / Cette thèse vise à comprendre les fondements et les fonctions des calculs probabilistes impliqués dans les processus visuels. Nous nous appuyons sur une double stratégie, qui implique le développement de modèles dans le cadre du codage prédictif selon le principe de l'énergie libre. Ces modèles servent à définir des hypothèses claires sur la fonction neuronale, qui sont testées à l'aide d'enregistrements extracellulaires du cortex visuel primaire. Cette région du cerveau est principalement impliquée dans les calculs sur les unités élémentaires des entrées visuelles naturelles, sous la forme de distributions d'orientations. Ces distributions probabilistes, par nature, reposent sur le traitement de la moyenne et de la variance d'une entrée visuelle. Alors que les premières ont fait l'objet d'un examen neurobiologique approfondi, les secondes ont été largement négligées. Cette thèse vise à combler cette lacune. Nous avançons l'idée que la connectivité récurrente intracorticale est parfaitement adaptée au traitement d'une telle variance d'entrées, et nos contributions à cette idée sont multiples. (1) Nous fournissons tout d'abord un examen informatique de la structure d'orientation des images naturelles et des stratégies d'encodage neuronal associées. Un modèle empirique clairsemé montre que le code neuronal optimal pour représenter les images naturelles s'appuie sur la variance de l'orientation pour améliorer l'efficacité, la performance et la résilience. (2) Cela ouvre la voie à une étude expérimentale des réponses neurales dans le cortex visuel primaire du chat à des stimuli multivariés. Nous découvrons de nouveaux types de neurones fonctionnels, dépendants de la couche corticale, qui peuvent être liés à la connectivité récurrente. (3) Nous démontrons que ce traitement de la variance peut être compris comme un graphe dynamique pondéré conditionné par la variance sensorielle, en utilisant des enregistrements du cortex visuel primaire du macaque. (4) Enfin, nous soutenons l'existence de calculs de variance (prédictifs) en dehors du cortex visuel primaire, par l'intermédiaire du noyau pulvinar du thalamus. Cela ouvre la voie à des études sur les calculs de variance en tant que calculs neuronaux génériques soutenus par la récurrence dans l'ensemble du cortex. / This thesis aims to understand the foundations and functions of the probabilistic computations involved in visual processes. We leverage a two-fold strategy, which involves the development of models within the framework of predictive coding under the free energy principle. These models serve to define clear hypotheses of neuronal function, which are tested using extracellular recordings of the primary visual cortex. This brain region is predominantly involved in computations on the elementary units of natural visual inputs, in the form of distributions of oriented edges. These probabilistic distributions, by nature, rely on processing both the mean and variance of a visual input. While the former have undergone extensive neurobiological scrutiny, the latter have been largely overlooked. This thesis aims to bridge this knowledge gap. We put forward the notion that intracortical recurrent connectivity is optimally suited for processing such variance of inputs, and our contributions to this idea are multi-faceted. (1) We first provide a computational examination of the orientation structure of natural images and associated neural encoding strategies. An empirical sparse model shows that the optimal neural code for representing natural images relies on orientation variance for increased efficiency, performance, and resilience. (2) This paves the way for an experimental investigation of neural responses in the cat's primary visual cortex to multivariate stimuli. We uncover novel, cortical-layer-dependent, functional neuronal types that can be linked to recurrent connectivity. (3) We demonstrate that this variance processing can be understood as a dynamical weighted graph conditioned on sensory variance, using macaque primary visual cortex recordings. (4) Finally, we argue for the existence of (predictive) variance computations outside the primary visual cortex, through the Pulvinar nucleus of the thalamus. This paves the way for studies on variance computations as generic weighting of neural computations, supported by recurrence throughout the entire cortex.

此篇論文，主要是討論遞迴式神經網路。在文中，我們將架構一個單層的神經網路結構。並利用三種不同的學習法則來套用此架構。我們也做了圓軌跡和圖形８的模擬，以及討論了此架構的收斂性。 / Our task in this paper is to discuss the Recurrent Neural Network. We construct a singal layer neural network and apply three different learning rules to simulate circular trajectory and figure eight. Also, we present the proof of convergence.

Dans un problème de prédiction à multiples pas discrets, la prédiction à chaque instant peut dépendre de l’entrée à n’importe quel moment dans un passé lointain. Modéliser une telle dépendance à long terme est un des problèmes fondamentaux en apprentissage automatique. En théorie, les Réseaux de Neurones Récurrents (RNN) peuvent modéliser toute dépendance à long terme. En pratique, puisque la magnitude des gradients peut croître ou décroître exponentiellement avec la durée de la séquence, les RNNs ne peuvent modéliser que les dépendances à court terme. Cette thèse explore ce problème dans les réseaux de neurones récurrents et propose de nouvelles solutions pour celui-ci. Le chapitre 3 explore l’idée d’utiliser une mémoire externe pour stocker les états cachés d’un réseau à Mémoire Long et Court Terme (LSTM). En rendant l’opération d’écriture et de lecture de la mémoire externe discrète, l’architecture proposée réduit le taux de décroissance des gradients dans un LSTM. Ces opérations discrètes permettent également au réseau de créer des connexions dynamiques sur de longs intervalles de temps. Le chapitre 4 tente de caractériser cette décroissance des gradients dans un réseau de neurones récurrent et propose une nouvelle architecture récurrente qui, grâce à sa conception, réduit ce problème. L’Unité Récurrente Non-saturante (NRUs) proposée n’a pas de fonction d’activation saturante et utilise la mise à jour additive de cellules au lieu de la mise à jour multiplicative. Le chapitre 5 discute des défis de l’utilisation de réseaux de neurones récurrents dans un contexte d’apprentissage continuel, où de nouvelles tâches apparaissent au fur et à mesure. Les dépendances dans l’apprentissage continuel ne sont pas seulement contenues dans une tâche, mais sont aussi présentes entre les tâches. Ce chapitre discute de deux problèmes fondamentaux dans l’apprentissage continuel: (i) l’oubli catastrophique d’anciennes tâches et (ii) la capacité de saturation du réseau. De plus, une solution est proposée pour régler ces deux problèmes lors de l’entraînement d’un réseau de neurones récurrent. / In a multi-step prediction problem, the prediction at each time step can depend on the input at any of the previous time steps far in the past. Modelling such long-term dependencies is one of the fundamental problems in machine learning. In theory, Recurrent Neural Networks (RNNs) can model any long-term dependency. In practice, they can only model short-term dependencies due to the problem of vanishing and exploding gradients. This thesis explores the problem of vanishing gradient in recurrent neural networks and proposes novel solutions for the same. Chapter 3 explores the idea of using external memory to store the hidden states of a Long Short Term Memory (LSTM) network. By making the read and write operations of the external memory discrete, the proposed architecture reduces the rate of gradients vanishing in an LSTM. These discrete operations also enable the network to create dynamic skip connections across time. Chapter 4 attempts to characterize all the sources of vanishing gradients in a recurrent neural network and proposes a new recurrent architecture which has significantly better gradient flow than state-of-the-art recurrent architectures. The proposed Non-saturating Recurrent Units (NRUs) have no saturating activation functions and use additive cell updates instead of multiplicative cell updates. Chapter 5 discusses the challenges of using recurrent neural networks in the context of lifelong learning. In the lifelong learning setting, the network is expected to learn a series of tasks over its lifetime. The dependencies in lifelong learning are not just within a task, but also across the tasks. This chapter discusses the two fundamental problems in lifelong learning: (i) catastrophic forgetting of old tasks, and (ii) network capacity saturation. Further, it proposes a solution to solve both these problems while training a recurrent neural network.

One of the many challenges of machine learning are systems for automatic tagging of music, the complexity of this issue in particular. These systems can be practically used in the content analysis of music or the sorting of music libraries. This thesis deals with the design, training, testing, and evaluation of artificial neural network architectures for automatic tagging of music. In the beginning, attention is paid to the setting of the theoretical foundation of this field. In the practical part of this thesis, 8 architectures of neural networks are designed (4 fully convolutional and 4 convolutional recurrent). These architectures are then trained using the MagnaTagATune Dataset and mel spectrogram. After training, these architectures are tested and evaluated. The best results are achieved by the four-layer convolutional recurrent neural network (CRNN4) with the ROC-AUC = 0.9046 ± 0.0016. As the next step of the practical part of this thesis, a completely new Last.fm Dataset 2020 is created. This dataset uses Last.fm and Spotify API for data acquisition and contains 100 tags and 122877 tracks. The most successful architectures are then trained, tested, and evaluated on this new dataset. The best results on this dataset are achieved by the six-layer fully convolutional neural network (FCNN6) with the ROC-AUC = 0.8590 ± 0.0011. Finally, a simple application is introduced as a concluding point of this thesis. This application is designed for testing individual neural network architectures on a user-inserted audio file. Overall results of this thesis are similar to other papers on the same topic, but this thesis brings several new findings and innovations. In terms of innovations, a significant reduction in the complexity of individual neural network architectures is achieved while maintaining similar results.

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Financial institutions today generate a large amount of data, data that can contain interesting information to investigate to further the economic growth of said institution. There exists an interest in analyzing these points of information, especially if they are anomalous from the normal day-to-day work. However, to find these outliers is not an easy task and not possible to do manually due to the massive amounts of data being generated daily. Previous work to solve this has explored the usage of machine learning to find outliers in these financial datasets. Previous studies have shown that the pre-processing of data usually stands for a big part in information loss. This work aims to study if there is a proper balance in how the pre-processing is carried out to retain the highest amount of information while simultaneously not letting the data remain too complex for the machine learning models. The dataset used consisted of Foreign exchange transactions supplied by the host company and was pre-processed through the use of Principal Component Analysis (PCA). The main purpose of this work is to test if an ensemble of Long Short-Term Memory Recurrent Neural Networks (LSTM), configured as autoencoders, can be used to detect outliers in the data and if the ensemble is more accurate than a single LSTM autoencoder. Previous studies have shown that Ensemble autoencoders can prove more accurate than a single autoencoder, especially when SkipCells have been implemented (a configuration that skips over LSTM cells to make the model perform with more variation). A datapoint will be considered an outlier if the LSTM model has trouble properly recreating it, i.e. a pattern that is hard to classify, making it available for further investigations done manually. The results show that the ensembled LSTM model proved to be more accurate than that of a single LSTM model in regards to reconstructing the dataset, and by our definition of an outlier, more accurate in outlier detection. The results from the pre-processing experiments reveal different methods of obtaining an optimal number of components for your data. One of those is by studying retained variance and accuracy of PCA transformation compared to model performance for a certain number of components. One of the conclusions from the work is that ensembled LSTM networks can prove very powerful, but that alternatives to pre-processing should be explored such as categorical embedding instead of PCA. / Finansinstitut genererar idag en stor mängd data, data som kan innehålla intressant information värd att undersöka för att främja den ekonomiska tillväxten för nämnda institution. Det finns ett intresse för att analysera dessa informationspunkter, särskilt om de är avvikande från det normala dagliga arbetet. Att upptäcka dessa avvikelser är dock inte en lätt uppgift och ej möjligt att göra manuellt på grund av de stora mängderna data som genereras dagligen. Tidigare arbete för att lösa detta har undersökt användningen av maskininlärning för att upptäcka avvikelser i finansiell data. Tidigare studier har visat på att förbehandlingen av datan vanligtvis står för en stor del i förlust av emphinformation från datan. Detta arbete syftar till att studera om det finns en korrekt balans i hur förbehandlingen utförs för att behålla den högsta mängden information samtidigt som datan inte förblir för komplex för maskininlärnings-modellerna. Det emphdataset som användes bestod av valutatransaktioner som tillhandahölls av värdföretaget och förbehandlades genom användning av Principal Component Analysis (PCA). Huvudsyftet med detta arbete är att undersöka om en ensemble av Long Short-Term Memory Recurrent Neural Networks (LSTM), konfigurerad som autoenkodare, kan användas för att upptäcka avvikelser i data och om ensemblen är mer precis i sina predikteringar än en ensam LSTM-autoenkodare. Tidigare studier har visat att en ensembel avautoenkodare kan visa sig vara mer precisa än en singel autokodare, särskilt när SkipCells har implementerats (en konfiguration som hoppar över vissa av LSTM-cellerna för att göra modellerna mer varierade). En datapunkt kommer att betraktas som en avvikelse om LSTM-modellen har problem med att återskapa den väl, dvs ett mönster som nätverket har svårt att återskapa, vilket gör datapunkten tillgänglig för vidare undersökningar. Resultaten visar att en ensemble av LSTM-modeller predikterade mer precist än en singel LSTM-modell när det gäller att återskapa datasetet, och då enligt vår definition av avvikelser, mer precis avvikelse detektering. Resultaten från förbehandlingen visar olika metoder för att uppnå ett optimalt antal komponenter för dina data genom att studera bibehållen varians och precision för PCA-transformation jämfört med modellprestanda. En av slutsatserna från arbetet är att en ensembel av LSTM-nätverk kan visa sig vara mycket kraftfulla, men att alternativ till förbehandling bör undersökas, såsom categorical embedding istället för PCA.